This document relates to data processing and verification.
The Internet provides access to a wide variety of resources, such as video and/or audio files, as well as web pages for particular subjects or particular news articles. Access to these resources has provided opportunities for advertisements to be provided with the resources. For example, web pages can include advertisement slots in which advertisements can be presented. The advertisements slots can be defined in the web page or defined for presentation with a web page, for example, in a pop-up window.
Advertisement slots can be allocated to advertisers through an auction. For example, advertisers can provide bids specifying amounts that the advertisers are respectively willing to pay for presentation of their advertisements. In turn, an auction can be performed and the advertisement slots can be allocated to advertisers according to their bids. For example, when one advertisement slot is being allocated in the auction, the advertisement slot can be allocated to the advertiser that provided the highest bid. When multiple advertisement slots are allocated in a single auction, the advertisement slots can be allocated to set of bidders that provided the highest bids.
The bids that advertisers provide for the auction are generally maintained in secret. For example, the advertisers can provide their respective bids to an auctioneer as sealed (e.g., encrypted) bids so that, even if the advertisers bid is intercepted by a third party, the value of the bid will remain concealed. Additionally, auction results that may be provided by an auctioneer can be provided in a manner that conceals the values of bids that were used in the auction. For example, the auctioneer may only announce the identity of the winning bidder. Thus, the advertiser typically relies on the auctioneer for assurance that the auction results are correct. When the advertiser relies solely on the auctioneer for correctness of auction results, it is possible that the auctioneer can manipulate the data to indicate that the auction results are correct even when the auction results were manipulated by the auctioneer.